Answer:
[tex]a_{n+1}=a_n+4[/tex]
Step-by-step explanation:
Have in mind the definition of the term [tex]a_n=4\,n-1[/tex], and now work on what the term [tex]a_{n+1}[/tex] is based on the previous definition:
[tex]a_{n+1} = 4\,(n+1)-1\\a_{n+1}=4\,n+4-1[/tex]
In the next step do NOT combine the numerical values, but try to identify the [tex]a_n[/tex] term ([tex]4\,n-1[/tex]) in the expression (notice the use of square brackets to group the relevant terms):
[tex]a_{n+1}=4\,n+4-1\\a_{n+1}=[4\,n-1]+4\\a_{n+1}=a_n+4[/tex]
So now we have the term "[tex]a_{n+1}[/tex]" defined in a recursive manner based on the previous term "[tex]a_n[/tex]"
